Calc III - Graphing a Function of Multiple Variables by hand

I come across questions where I have to match the equation with its contour map and graph.

Examples:

z = sin(xy)

z = sin(x-y)

Right now I'm using Wolfram Alpha for all of these, but supposing these appear on an exam... how do I graph it by hand? For example, for z = sin(xy) I'm just plugging in random values for x and y... but doesn't that mean the entire xy graph should be filled then?

I come across questions where I have to match the equation with its contour map and graph.

Examples:

z = sin(xy)

z = sin(x-y)

Right now I'm using Wolfram Alpha for all of these, but supposing these appear on an exam... how do I graph it by hand? For example, for z = sin(xy) I'm just plugging in random values for x and y... but doesn't that mean the entire xy graph should be filled then?

Set z equal to some value (-1 ≤ z ≤ 1, why?), then solve for y in terms of x.